Jeremy Corbyn at a campaign rally at the Arts Centre Theatre in Aberdeen.

The Labour leadership frontrunner, Jeremy Corbyn, has said he does not do “personal, reaction or abuse”, after dire warnings from Tony Blair and Yvette Cooper about the prospect of his leading the party.

Corbyn said life was too short to respond and the attitude devalued the political process, after fellow candidate Cooper said his polices were not credible and could split the party, and the former prime minister Blair said his ideas could lead Labour to annihilation.

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Asked about the comments, Corbyn, the MP for Islington North, told the Guardian: “We’re in the midst of the biggest democratic process that the Labour party has ever been involved with. Hundreds of thousands of people are party members and union supporters and registered supporters, a lot of them are young people who’ve never been involved in party politics before but involved in other activities like the environment or peace or student issues, and older people who have come back to Labour.

“Shouldn’t we be happy about that? Shouldn’t we be happy that it’s a popular discussion and a popular debate, and a choice will be made. And after 12 September , whoever wins the election, there’s going to have to be a big discussion about the policy direction of our party: on austerity, on Trident, on many many other issues. We’ve used this campaign to put forward policy issues on the economy, the environment, arts policy.

“We’re the one putting forward ideas, so I don’t do personal, I don’t do reaction, I don’t do abuse. Life is too short and it devalues the political process. I think we should try and enhance the democratic life of this country, not reduce it to that level.”

Corbyn is now the clear favourite to win the contest, according to polls and internal data from at least three of the campaigns.

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Andy Burnham, the MP for Leigh, and Cooper (who represents Normanton, Pontefract and Castleford) are battling for second place, while Liz Kendall, MP for Leicester West, appears to be trailing last.

Corbyn’s chances have been boosted by a tripling in Labour membership and registered supporters, since the election, to more than 600,000. Around 190,000 have been recruited through trade unions, with between 90,000 and 100,000 thought to have come through Unite.

Len McCluskey, leader of Unite, will, over the weekend, be writing to his members who are signed up reiterating the union’s official position, which is a vote for Corbyn and a second preference for Burnham.

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Outlining what she described as her feminist vision for Labour, Cooper said Corbyn was proposing economic policies that could increase inflation, cut investment and undermine growth.

However, Burnham hit out at those making attacks on Corbyn, saying this misread the mood of the party. In an interview with the BBC’s World at One, which was dominated by questions about Corbyn, Burnham warned against Labour figures dismissing the frontrunner and suggested he could serve in the team of any of his rivals if they were to win.

Burnham said he believed his own campaign showed he was the only candidate who could unite the party, but he also praised Corbyn for having brought the contest to life. “The attacks we’ve seen on Jeremy misread the mood of the party because what people are crying out for is something different. They are fed up with the way Labour has been conducting policies in recent times,” he said.

He criticised Blair in particular, saying it was not helpful for former prime ministers to “second-guess the outcome and to make these dire predictions on the back of it”.

He added: “I will be keeping it positive. I want to get my case over to the 600,000 people who have a vote in this contest. They will rightly decide the future of the Labour party now. I think people are well aware of the issues at stake and I think the time has come to trust the members of our party and the supporters of our party to make the right decision about its future.”

Despite his campaign having participated in a letter with Cooper and Kendall’s teams raising concern about the way the contest has been conducted, he said it was “not the time to cry foul on the rules”.

He said: “It should be a cause for celebration that the Labour party has the ability to bring 600,000 people into its leadership election. I think it is a positive thing that there is a vibrant contest and that there are a wide number of people from different walks of life able to have a say.”